Medieval Muslims Made Early Math Breakthrough
Magnificently sophisticated geometric patterns in medieval Islamic architecture indicate their designers achieved a mathematical breakthrough 500 years earlier than Western scholars, scientists said on Thursday.
By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasi-crystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.
Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasi-crystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.
"Oh, it's absolutely stunning," Lu said in an interview. "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years."
Lu and Steinhardt in particular cite designs on the Darb-i Imam shrine in Isfahan, Iran, built in 1453.
Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns. The walls of many medieval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs.
"You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex" over time, Lu added.
While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas.
Lu said the new revelations suggest Islamic culture was even more advanced than previously thought. While travelling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasi-crystalline Islamic tilings.
The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide. Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasi-crystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran.
Joshua Socolar, a Duke university physicist, said it is unclear whether the medieval Islamic artisans fully understood the mathematical properties of the patterns they were making. "It leads you to wonder whether they kind of got lucky," Socolar said in an interview. "But the fact remains that the patterns are tantalisingly close to having the structure that Penrose discovered in the mid-70s. And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show," Socolar said. (Will Dunham, Independent Online)
Image Source: The pattern on the Darb-i Imam shrine
By the 15th century, decorative tile patterns on these masterpieces of Islamic architecture reached such complexity that a small number boasted what seem to be "quasi-crystalline" designs, Harvard University's Peter Lu and Princeton University's Paul Steinhardt wrote in the journal Science.
Only in the 1970s did British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasi-crystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry.
"Oh, it's absolutely stunning," Lu said in an interview. "They made tilings that reflect mathematics that were so sophisticated that we didn't figure it out until the last 20 or 30 years."
Lu and Steinhardt in particular cite designs on the Darb-i Imam shrine in Isfahan, Iran, built in 1453.
Islamic tradition has frowned upon pictorial representations in artwork. Mosques and other grand buildings erected by Islamic architects throughout the Middle East, Central Asia and elsewhere often are wrapped in rich, intricate tile designs setting out elaborate geometric patterns. The walls of many medieval Islamic structures display sumptuous geometric star-and-polygon patterns. The research indicated that by 1200 an important breakthrough had occurred in Islamic mathematics and design, as illustrated by these geometric designs.
"You can go through and see the evolution of increasing geometric sophistication. So they start out with simple patterns, and they get more complex" over time, Lu added.
While Europe was mired in the Dark Ages, Islamic culture flourished beginning in the 7th century, with achievements over numerous centuries in mathematics, medicine, engineering, ceramics, art, textiles, architecture and other areas.
Lu said the new revelations suggest Islamic culture was even more advanced than previously thought. While travelling in Uzbekistan, Lu said, he noticed a 16th century Islamic building with decagonal motif tiling, arousing his curiosity as to the existence of quasi-crystalline Islamic tilings.
The sophistication of the patterns used in Islamic architecture has intrigued scholars worldwide. Emil Makovicky of the University of Copenhagen in Denmark in the 1990s noticed the relationship between these designs and a form of quasi-crystalline designs. Makovicky was interested in particular in an 1197 tomb in Maragha, Iran.
Joshua Socolar, a Duke university physicist, said it is unclear whether the medieval Islamic artisans fully understood the mathematical properties of the patterns they were making. "It leads you to wonder whether they kind of got lucky," Socolar said in an interview. "But the fact remains that the patterns are tantalisingly close to having the structure that Penrose discovered in the mid-70s. And it will be a lot of fun if somebody turns up bigger tilings that sort of make a more convincing case that they understood even more of the geometry than the present examples show," Socolar said. (Will Dunham, Independent Online)
Image Source: The pattern on the Darb-i Imam shrine
Labels: World .
1 Comments:
Please check out thoroughly the sources of influence and even direct tutelage for 'Arabic' cosmology. It is Indian and vedic. For example: from the online encylcoapeadia Bitannica:
http://concise.britannica.com/ebc/article-9016154/Brahmagupta
http://www-history.mcs.st-andrews.ac.uk/Projects/Pearce/Chapters/Ch8_3.html
One of the most accomplished of the ancient Indian astronomers. He also had a profound and direct influence on Islamic and Byzantine astronomy.
Brahmagupta was an orthodox Hindu, and his religious views, particularly the Hindu yuga system of measuring the ages of mankind, influenced his work....
Brahmagupta's fame rests mostly on his Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”), an astronomical work that he probably wrote while living in Bhillamala, then the capital of the Gurjara-Pratihara dynasty. It was translated into Arabic in Baghdad about 771 and had a major impact on Islamic mathematics and astronomy. Late in his life, Brahmagupta wrote Khandakhadyaka (665; “A Piece Eatable”), an astronomical handbook that employed Aryabhata's system of starting each day at midnight.
In addition to expounding on traditional Indian astronomy in his books, Brahmagupta devoted several chapters of Brahma-sphuta-siddhanta to mathematics. In chapters 12 and 18 in particular, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations), which roughly correspond to arithmetic (including mensuration) and algebra, respectively. Chapter 12 is simply named “Mathematics,” probably because the “basic operations,” such as arithmetic operations and proportions, and the “practical mathematics,” such as mixture and series, treated there occupied the major part of the mathematics of Brahmagupta's milieu. He stressed the importance of these topics as a qualification for a mathematician, or calculator (ganaka). Chapter 18, “Pulverizer,” is named after the first topic of the chapter, probably because no particular name for this area (algebra) existed yet.
Among his major accomplishments, Brahmagupta defined zero as the result of subtracting a number from itself and gave rules for arithmetical operations among negative numbers (“debts”) and positive numbers (“property”), as well as surds. He also gave partial solutions to certain types of indeterminate equations of the second degree with two unknown variables. Perhaps his most famous result was a formula for the area of a cyclic quadrilateral (a four-sided polygon whose vertices all reside on some circle) and the length of its diagonals in terms of the length of its sides. He also gave a valuable interpolation formula for computing sines.
-Takao Hayashi
Also 'Arabic 'numerals are also vedic Sanskrit Indian and misnamed as Arabic.
Post a Comment
<< Home